Suppose the signal x ∈ Rn is realized by driving a d-sparse signal z ∈ Rn through an arbitrary unknown
stable discrete-linear time invariant system H, namely, x(t) = (h * z)(t), where h(·) is the impulse response of
the operator H. Is x(·) compressible in the conventional sense of compressed sensing? Namely, can x(t) be
reconstructed from sparse set of measurements. For the case when the unknown system H is auto-regressive (i.e.
all pole) of a known order it turns out that x can indeed be reconstructed from O(k log(n)) measurements. The
main idea is to pass x through a linear time invariant system G and collect O(k log(n)) sequential measurements.
The filter G is chosen suitably, namely, its associated Toeplitz matrix satisfies the RIP property. We develop a
novel LP optimization algorithm and show that both the unknown filter H and the sparse input z can be reliably
estimated. These types of processes arise naturally in Reflection Seismology.
Network video cameras, invented in the last decade or so, permit today pervasive, wide-area visual surveillance. However, due to the vast amounts of visual data that such cameras produce human-operator monitoring is not possible and automatic algorithms are needed. One monitoring task of particular interest is the detection of
suspicious behavior, i.e., identification of individuals or objects whose behavior differs from behavior usually observed. Many methods based on object path analysis have been developed to date (motion detection followed by tracking and inferencing) but they are sensitive to motion detection and tracking errors and are also computationally complex. We propose a new surveillance method capable of abnormal behavior detection without explicit estimation of object paths. Our method is based on a simple model of video dynamics. We propose one practical implementation of this general model via temporal aggregation of motion detection labels. Our method requires
little processing power and memory, is robust to motion segmentation errors, and general enough to monitor humans, cars or any other moving objects in uncluttered as well as highly-cluttered scenes. Furthermore, on account of its simplicity, our method can provide performance guarantees. It is also robust in harsh environments
(jittery cameras, rain/snow/fog).